Shakedown of elasto-plastic continnua with special reference to soil-rock structures

The recent activity in the design and construction of off-shore structures has imparted considerable impetus to research on the behaviour of soils in cyclic loading. Many new constitutive models for soil behaviour have been presented in recent years ( Mroz, Norris and Zienkiewicz, 1978 ; Bazant and Krizak, 1976 ). They attempt at simulating the experimentally observed failure of soils due to cycling of the load. Soils are complex two-phase materials but even for simpler ideal elasto∕ plastic materials, the solution of shakedown under cyclic loading for the situations of interest to geotechnical engineers are not available. Though structural engineers have been aware of this problem for considerable time and have evolved their design criteria for safety against fatigue failure of structural elements, the only exact solution available for a continuum is that of a thick cylinder subjected to fluctuating internal pressure ( Symond and Neal, 1951 ; Symond, 1952) Zienkiewicz et al (1976) were the first to point out the possibility of progressive settlement of a footing under a particular system of cyclic loads. Their conclusions were based on repeated number of finite element analyses. The authors have attempted here to obtain approximate solutions of shakedown loads on strip footings subjected to repeated vertical and horizontal loads and moments for certain specified load paths, using very few finite element analyses in conjunction with shakedown theorems ( Melan, 1938 ). The results are presented in the form of design graphs.